431 Class 02

Thomas E. Love, Ph.D.

2024-08-29

Instructions for the Quick Survey

Please read these instructions before writing.

Introduce yourself to someone that you don’t know.
Record the survey answers for that other person, while they record your responses.
Be sure to complete all 15 questions (both sides.)
When you are finished, thank your partner and raise your hand. Someone will come to collect your survey.

Regarding Question 4, Professor Love is the large fellow standing in the front of the room.

Today’s Agenda

Data Structures and Variables
- Evaluating some of the Quick Survey variables
Looking at some of the data collected in Class 01
- Group Guessing of Ages from 10 Photographs
- Guessing Dr. Love’s Age (twice)
Welcome to 431 Survey Report
What to work on this weekend

The R Packages I’ll Load Today

library(janitor)
library(rstanarm)
library(easystats)
library(tidyverse)

source("c02/data/Love-431.R")

knitr::opts_chunk$set(comment = NA)

If you actually run this in R, you will get some messages which we will suppress and ignore today.

Chatfield’s Six Rules for Data Analysis

Do not attempt to analyze the data until you understand what is being measured and why.
Find out how the data were collected.
Look at the structure of the data.
Carefully examine the data in an exploratory way, before attempting a more sophisticated analysis.
Use your common sense at all times.
Report the results in a clear, self-explanatory way.

Our Quick Survey

Types of Data

The key distinction we’ll make is between

quantitative (numerical) and
categorical (qualitative) information.

Information that is quantitative describes a quantity.

All quantitative variables have units of measurement.
Quantitative variables are recorded in numbers, and we use them as numbers (for instance, taking a mean of the variable makes some sense.)

Continuous vs. Discrete Quantities

Continuous variables (can take any value in a range) vs. Discrete variables (limited set of potential values)

Is Height a continuous or a discrete variable?

Height is certainly continuous as a concept, but how precise is our ruler?
Piano vs. Violin

Quantitative Variable Subtypes

We can also distinguish interval (equal distance between values, but zero point is arbitrary) from ratio variables (meaningful zero point.)

Is Weight an interval or ratio variable?
How about IQ?

Qualitative (Categorical) Data

Qualitative variables consist of names of categories.

Each possible value is a code for a category (could use numerical or non-numerical codes.)
- Binary categorical variables (two categories, often labeled 1 or 0)
- Multi-categorical variables (three or more categories)
Can distinguish nominal (no underlying order) vs. ordinal (categories are ordered.)

Some Categorical Variables

How is your overall health?
(Excellent, Very Good, Good, Fair, Poor)
Which candidate would you vote for if the election were held today?
Did this patient receive this procedure?
If you needed to analyze a small data set right away, which of the following software tools would you be comfortable using to accomplish that task?

Are these quantitative or categorical?

Do you smoke? (1 = Non-, 2 = Former, 3 = Smoker)
How much did you pay for your most recent haircut? (in $)
What is your favorite color?
How many hours did you sleep last night?
Statistical thinking in your future career? (1 = Not at all important to 7 = Extremely important)

If quantitative, are they discrete or continuous? Do they have a meaningful zero point?
If categorical, how many categories? Nominal or ordinal?

Importing and Tidying Data

Ingesting the Quick Surveys

The Quick Survey

Over 10 years, 547 people took (essentially) the same survey in the same way.

Fall	2023	2022	2021	2020	2019
n	53	54	58	67	61

Fall	2018	2017	2016	2015	2014	Total
n	51	48	64	49	42	547

Question

About how many of those 547 surveys caused no problems in recording responses?

The 15 Survey Items

#	Topic	#	Topic
Q1	`glasses`	Q9	`lectures_vs_activities`
Q2	`english`	Q10	`projects_alone`
Q3	`stats_so_far`	Q11	`height`
Q4	`guess_TL_ht`	Q12	`hand_span`
Q5	`smoke`	Q13	`color`
Q6	`handedness`	Q14	`sleep`
Q7	`stats_future`	Q15	`pulse_rate`
Q8	`haircut`	-	-

At one time, I asked about sex rather than glasses.
In prior years, people guessed my age, rather than height here.
Sometimes, I’ve asked for a 30-second pulse check, then doubled.

Response to the Question I asked

About how many of those 547 surveys caused no problems in recording responses?

Guesses?

196/547 (36%) caused no problems.

Guess My Age

What should we do in these cases?

English best language?

Height

Handedness Scale (2016-21 version)

Favorite color

Following the Rules? (2019 version)

2019 `pulse` responses, sorted (n = 61, 1 NA)

 33  46  48  56  60  60            3 | 3
 62  63  65  65  66  66            4 | 68
 68  68  68  69  70  70            5 | 6
 70  70  70  70  70  70            6 | 002355668889        
 71  72  72  74  74  74            7 | 00000000122444445666888
 74  74  75  76  76  76            8 | 000012445668
 78  78  78  80  80  80            9 | 000046
 80  81  82  84  84  85           10 | 44
 86  86  88  90  90  90           11 | 0
 90  94  96 104 104 110

Stem and Leaf: Pulse Rates 2014-2023

(Thanks, John Tukey )

Garbage in, garbage out …

Group Age Guessing from Photos
(13 groups, 10 Photos)

Photos 1-5

Photos 6-10

2024 Groups 1-6: Guessing Ten Photos

Group	Within 2	Within 5	Too Low	Correct	Too High	Beat AI
The Confident Interval	3	5	1	1	8	6
MAWC	3	7	4	1	5	7
The Renaissance Coders	1	7	2	1	7	6
R-rational	2	6	5	1	4	7
TVMB	6	9	1	1	8	7
Something Creative & Original	2	5	5	1	4	5
AI	2	4	7	1	2	–

These six groups (and the AI at https://howolddoyoulook.com/) each guessed one age correctly. The other seven groups are shown on the next slide.

2024 Groups 7-13: Ten Photos

Group	Within 2	Within 5	Too Low	Too High	Beat AI
Baked Split	4	8	3	7	6
Pineapple Pizza	4	8	5	5	7
CWRU Crew	4	4	5	5	6
Statasaurous rex	2	6	3	7	5
Tukey 60	3	8	4	6	5
Beat the Curve	0	5	4	6	5
Stats Avengers	4	6	3	7	5

So … who wins?
What other summaries might be helpful?

Error Distribution, Groups 1-6

Group	Mean Error	SD (Errors)	Median Error	(Min, Max) Error
The Confident Interval	5	7.3	3	-8, 16
MAWC	1	7	1	-11, 14
The Renaissance Coders	2.6	6.1	4	-9, 13
R-rational	0.8	5.6	-1	-6, 10
TVMB	2	2.5	1	-2, 7
Something Creative and Original	-0.2	6.2	-0.5	-8, 8
AI	-5	7.3	-5.5	-15, 6

Error Distribution, Groups 7/13

Group	Mean Error	SD (Errors)	Median Error	(Min, Max) Error
Baked Split	3.4	5.7	2	-3, 14
Pineapple Pizza	1	6.3	0.5	-6, 16
CWRU Crew	-2	7.3	0	-13, 9
Statasaurous rex	1.8	5.7	4	-10, 8
Tukey 60	2.1	6.3	1	-5, 16
Beat the Curve	2	7.5	3.5	-8, 13
Stats Avengers	1.9	9.4	3	-21, 15

How helpful are these summaries in this setting?
Should we be looking at |error| or maybe squared error?

Absolute and Squared Errors (first 6)

AE = Absolute Value of Error = |guess - actual|
RMSE = square Root of Mean Squared Error

Group	Mean AE	Range (AE)	Median AE	RMSE
The Confident Interval	6.6	0, 16	5.5	8.5
MAWC	5.2	0, 14	3.5	6.7
The Renaissance Coders	5.4	0, 13	4.5	6.3
R-rational	4.6	0, 10	4.5	5.3
TVMB	2.4	0, 7	1.5	3.1
Something Creative and Original	5.2	0, 8	5.5	5.9
AI	7	0, 15	6	8.5

Absolute and Squared Errors (7-13)

AE = Absolute Value of Error = |guess - actual|
RMSE = square Root of Mean Squared Error

Group	Mean AE	Range (AE)	Median AE	RMSE
Baked Split	4.4	1, 14	3	6.4
Pineapple Pizza	4.4	1, 16	3	6
CWRU Crew	5.8	1, 13	6	7.2
Statasaurous rex	5.2	2, 10	5	5.7
Tukey 60	4.7	1, 16	4	6.4
Beat the Curve	6.6	3, 13	5.5	7.4
Stats Avengers	6.5	1, 21	4	9.1
AI	7	0, 15	6	8.5

So … now who wins?

Importing guesses from 2014-2024

photos <- 
  read_csv("c02/data/ten-photo-age-history-2024.csv",
           show_col_types = F)

photos <- photos |>
  mutate(label = fct_reorder(label, card))

head(photos)

# A tibble: 6 × 13
  order  card label   age sex   facing year  mean_guess error abs_error sq_error
  <dbl> <dbl> <fct> <dbl> <chr> <chr>  <chr>      <dbl> <dbl>     <dbl>    <dbl>
1     1     1 Chong    21 M     R      2024        25.3   4.3       4.3    18.5 
2     2     2 Arch…    64 F     L      2024        56.8  -7.2       7.2    51.8 
3     3     3 Mayf…    28 F     L      2024        31.4   3.4       3.4    11.6 
4     4     4 Love     14 M     L      2024        15.1   1.1       1.1     1.21
5     5     5 McGi…    54 F     R      2024        63.5   9.5       9.5    90.2 
6     6     6 Chan…    74 M     L      2024        72.9  -1.1       1.1     1.21
# ℹ 2 more variables: `detailed description` <chr>, jpeg <chr>

2014-2024 Errors

Guessing My Age (Twice)
from Class 01

From our 431-Data Page: A `.csv` file

I’ve placed love-age-guesses-2022-2024.csv on our 431-data page. This includes guesses from 2022-2024.

Creating the `age_guess` Tibble

Clicking on RAW in the 431-data presentation takes us to a (long) URL that contains the raw data in this sheet.

I’ll read in the sheet’s data to a new tibble (a special kind of R data frame) called age_guess using the read_csv() function.

url_age <- 
  "https://raw.githubusercontent.com/THOMASELOVE/431-data/main/data/love-age-guesses-2022-2024.csv"

age_guess <- read_csv(url_age, show_col_types = FALSE)

The `age_guess` tibble

What do we get?

age_guess

# A tibble: 148 × 5
   student   guess1 guess2 actual  year
   <chr>      <dbl>  <dbl>  <dbl> <dbl>
 1 S-2022-01     57     62   55.5  2022
 2 S-2022-02     53     53   55.5  2022
 3 S-2022-03     50     50   55.5  2022
 4 S-2022-04     48     56   55.5  2022
 5 S-2022-05     61     NA   55.5  2022
 6 S-2022-06     63     63   55.5  2022
 7 S-2022-07     67     58   55.5  2022
 8 S-2022-08     50     57   55.5  2022
 9 S-2022-09     50     50   55.5  2022
10 S-2022-10     43     56   55.5  2022
# ℹ 138 more rows

How many guesses in each year?

age_guess |> count(year)

# A tibble: 3 × 2
   year     n
  <dbl> <int>
1  2022    53
2  2023    39
3  2024    56

How many first guesses in each year were less than 57.5?

age_guess |> count(year, guess1 < 57.5)

# A tibble: 6 × 3
   year `guess1 < 57.5`     n
  <dbl> <lgl>           <int>
1  2022 FALSE              14
2  2022 TRUE               39
3  2023 FALSE              11
4  2023 TRUE               28
5  2024 FALSE              26
6  2024 TRUE               30

What do the `guess1` values look like?

age_guess |> 
  select(guess1) |> 
  arrange(guess1)

# A tibble: 148 × 1
   guess1
    <dbl>
 1     40
 2     40
 3     42
 4     42
 5     43
 6     44
 7     44
 8     45
 9     45
10     45
# ℹ 138 more rows

Plot the `guess1` values?

ggplot(data = age_guess, 
       aes(x = guess1)) +
  geom_dotplot(binwidth = 1)

Can we make a histogram?

ggplot(age_guess, 
       aes(x = guess1)) +
  geom_histogram()

Improving the Histogram, 1

ggplot(age_guess, 
       aes(x = guess1)) +
  geom_histogram(bins = 10)

Improving the Histogram, 2

ggplot(age_guess, 
       aes(x = guess1)) +
  geom_histogram(bins = 10, 
        col = "yellow")

Improving the Histogram, 3

ggplot(age_guess, 
       aes(x = guess1)) +
  geom_histogram(bins = 10, 
       col = "white", 
       fill = "blue")

Improving the Histogram, 3

Improving the Histogram, 4

Change theme, specify bin width rather than number of bins

ggplot(age_guess, 
       aes(x = guess1)) +
  geom_histogram(binwidth = 2, 
       col = "white", fill = "blue") +
  theme_bw()

Improving the Histogram, 4

Improving the Histogram, 5

ggplot(age_guess, 
       aes(x = guess1)) +
  geom_histogram(binwidth = 2, 
       col = "white", fill = "blue") +
  theme_bw() +
  labs(
    x = "First Guess of Dr. Love's Age",
    y = "Fall 2022-2024 431 students")

Improving the Histogram, 5

Add title and subtitle (ver. 6)

ggplot(age_guess, 
       aes(x = guess1)) +
  geom_histogram(binwidth = 2, 
       col = "white", fill = "blue") +
  theme_bw() +
  labs(
    x = "First Guess of Dr. Love's Age",
    y = "Fall 2022-2024 431 students",
    title = "Pretty wide range of guesses",
    subtitle = "Dr. Love's Actual Age = 55.5 in 2022, 57.5 in 2024")

Add title and subtitle (ver. 6)

Improving the Histogram, 7

Add a vertical line at 57.5 years to show my actual age.

ggplot(age_guess, 
       aes(x = guess1)) +
  geom_histogram(binwidth = 2, 
       col = "white", fill = "blue") +
  geom_vline(aes(xintercept = 56), col = "red") +
  theme_bw() +
  labs(
    x = "First Guess of Dr. Love's Age",
    y = "Fall 2022-2024 431 students",
    title = "Pretty wide range of guesses",
    subtitle = "Dr. Love's Actual Age = 55.5 in 2022, 57.5 in 2024")

Improving the Histogram, 7

In which year did I look older?

Create three facets, for 2022, 2023 and 2024 guesses…

ggplot(age_guess, 
       aes(x = guess1, fill = factor(year))) +
  geom_histogram(binwidth = 2, col = "white") +
  theme_bw() +
  facet_grid(year ~ .) +
  labs(
    x = "First Guess of Dr. Love's Age",
    y = "# of Students",
    title = "Distribution of guesses over the past three years",
    subtitle = "Dr. Love's Actual Age = 55.5 in 2022, 57.5 in 2024")

In which year did I look older?

Numerical Summary

age_guess |> select(student, guess1, guess2, year) |> summary()

   student              guess1          guess2           year     
 Length:148         Min.   :40.00   Min.   :40.00   Min.   :2022  
 Class :character   1st Qu.:50.00   1st Qu.:53.00   1st Qu.:2022  
 Mode  :character   Median :55.00   Median :56.00   Median :2023  
                    Mean   :54.65   Mean   :56.08   Mean   :2023  
                    3rd Qu.:58.00   3rd Qu.:59.00   3rd Qu.:2024  
                    Max.   :72.00   Max.   :70.00   Max.   :2024  
                                    NA's   :3

Was the average guess closer on guess 1 or 2?
What was the range of first guesses? Second guesses?
What does the NA's : 3 mean in guess2?
Why is student not summarized any further?

Let’s Focus on 2024 guesses

age_24 <- age_guess |>
  filter(year == "2024")

age_24

# A tibble: 56 × 5
   student   guess1 guess2 actual  year
   <chr>      <dbl>  <dbl>  <dbl> <dbl>
 1 S-2024-01     45     53   57.5  2024
 2 S-2024-02     50     55   57.5  2024
 3 S-2024-03     65     62   57.5  2024
 4 S-2024-04     55     60   57.5  2024
 5 S-2024-05     65     67   57.5  2024
 6 S-2024-06     58     56   57.5  2024
 7 S-2024-07     58     56   57.5  2024
 8 S-2024-08     60     55   57.5  2024
 9 S-2024-09     56     53   57.5  2024
10 S-2024-10     62     58   57.5  2024
# ℹ 46 more rows

First Guesses in 2024

age_24 |> select(guess1) |> table()

guess1
44 45 46 47 48 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 
 1  1  1  2  1  4  1  2  3  1  5  5  3  6  6  4  1  3  1  1  2  1  1

Simple Stem-and-Leaf

4 | 4
4 | 56778
5 | 00001223334
5 | 5555566666777888888999999
6 | 0000122234
6 | 5567

age_24 |> select(guess1) |> summary()

     guess1     
 Min.   :44.00  
 1st Qu.:53.00  
 Median :57.00  
 Mean   :56.25  
 3rd Qu.:59.25  
 Max.   :67.00

Summarizing 2024 Guesses

describe_distribution(age_24 |> select(guess1, guess2), ci = 0.90)

Variable |  Mean |   SD |  IQR |         90% CI |          Range | Skewness | Kurtosis |  n | n_Missing
-------------------------------------------------------------------------------------------------------
guess1   | 56.25 | 5.39 | 6.75 | [55.01, 57.39] | [44.00, 67.00] |    -0.31 |    -0.25 | 56 |         0
guess2   | 57.61 | 4.55 | 5.75 | [56.62, 58.34] | [47.00, 67.00] |    -0.07 |    -0.06 | 56 |         0

Mean = sum of values divided by number of values
Standard Deviation = square root of variance, measure of variation
IQR = difference between 75th and 25th percentiles
90% confidence interval for mean estimated via bootstrap
Range = minimum and maximum values
n = sample size
n_Missing = # of missing values

Summarizing 2024 Guesses

describe_distribution(age_24 |> select(guess1, guess2), 
                      centrality = "median", ci = 0.90, 
                      range = FALSE, quartiles = TRUE)

Variable | Median |  MAD |  IQR |         90% CI |    Quartiles | Skewness | Kurtosis |  n | n_Missing
------------------------------------------------------------------------------------------------------
guess1   |  57.00 | 4.45 | 6.75 | [55.98, 58.00] | 53.00, 59.25 |    -0.31 |    -0.25 | 56 |         0
guess2   |  57.50 | 3.71 | 5.75 | [57.00, 59.00] | 55.00, 60.25 |    -0.07 |    -0.06 | 56 |         0

Median = 50th percentile (middle value when data are sorted)
90% CI here is a bootstrap 90% confidence interval for the median
MAD = median absolute deviation (scaled to take the same value as the standard deviation when the data are Normally distributed)
Quartiles = 25th and 75th percentiles

Summarizing 2024 Guesses

Using the lovedist() function from the Love-431.R script

age_24 |>
  reframe(lovedist(guess1))

# A tibble: 1 × 10
      n  miss  mean    sd   med   mad   min   q25   q75   max
  <int> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1    56     0  56.2  5.39    57  4.45    44    53  59.2    67

age_24 |>
  reframe(lovedist(guess2))

# A tibble: 1 × 10
      n  miss  mean    sd   med   mad   min   q25   q75   max
  <int> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1    56     0  57.6  4.55  57.5  3.71    47    55  60.2    67

How did guesses change in 2024?

Did your guesses decrease / stay the same / increase?
Calculate guess2 - guess1 and examine its sign.

age_guess |> 
  filter(year == "2024") |>
  count(sign(guess2 - guess1))

# A tibble: 3 × 2
  `sign(guess2 - guess1)`     n
                    <dbl> <int>
1                      -1    14
2                       0    14
3                       1    28

How much did guesses change in 2024?

Create new variable (change = guess2 - guess1)

age_guess <- age_guess |>
  mutate(change = guess2 - guess1)

age_guess |> filter(year == "2024") |> select(change) |> summary()

     change      
 Min.   :-8.000  
 1st Qu.:-0.250  
 Median : 0.500  
 Mean   : 1.357  
 3rd Qu.: 4.000  
 Max.   :17.000

Histogram of Guess Changes

What will this look like?

ggplot(data = age_guess, aes(x = change)) +
  geom_histogram(binwidth = 2, fill = "royalblue", col = "yellow") + 
  theme_bw() +
  labs(x = "Change from first to second guess",
       y = "Students in 431 for Fall 2022-2024",
       title = "Most stayed close to their first guess.")

Histogram of Guess Changes

Guess 1 vs. Guess 2 Scatterplot

ggplot(data = age_guess, aes(x = guess1, y = guess2)) +
  geom_point()

Filter to complete cases, and add regression line

temp <- age_guess |>
  filter(complete.cases(guess1, guess2))

ggplot(data = temp, aes(x = guess1, y = guess2)) +
  geom_point() +
  geom_smooth(method = "lm", formula = y ~ x, col = "purple")

Filter to complete cases, and add regression line

What is that regression line?

lm(guess2 ~ guess1, data = age_guess)


Call:
lm(formula = guess2 ~ guess1, data = age_guess)

Coefficients:
(Intercept)       guess1  
    22.6760       0.6118

Note that lm filters to complete cases by default.

Bayesian linear regression instead?

set.seed(431)
stan_glm(guess2 ~ guess1, data = age_guess, refresh = 0)

stan_glm
 family:       gaussian [identity]
 formula:      guess2 ~ guess1
 observations: 145
 predictors:   2
------
            Median MAD_SD
(Intercept) 22.8    2.7  
guess1       0.6    0.0  

Auxiliary parameter(s):
      Median MAD_SD
sigma 3.7    0.2   

------
* For help interpreting the printed output see ?print.stanreg
* For info on the priors used see ?prior_summary.stanreg

How about a loess smooth curve?

temp <- age_guess |>
  filter(complete.cases(guess1, guess2))

ggplot(data = temp, aes(x = guess1, y = guess2)) +
  geom_point() +
  geom_smooth(method = "loess", formula = y ~ x, col = "blue") +
  theme_bw()

How about a loess smooth curve?

Add y = x line (no change in guess)?

temp <- age_guess |>
  filter(complete.cases(guess1, guess2))

ggplot(data = temp, aes(x = guess1, y = guess2)) +
  geom_point() +
  geom_smooth(method = "loess", formula = y ~ x, col = "blue") +
  geom_abline(intercept = 0, slope = 1, col = "red") +
  theme_bw()

Add y = x line (no change in guess)?

2024 Data, With Better Labels

ggplot(data = temp |> filter(year == "2024"), aes(x = guess1, y = guess2)) +
  geom_point() +
  geom_smooth(method = "loess", formula = y ~ x, col = "blue") +
  geom_abline(intercept = 0, slope = 1, col = "red") +
  geom_text(x = 47, y = 45, label = "y = x", col = "red") +
  labs(x = "First Guess of Love's Age",
       y = "Second Guess of Love's Age",
       title = "Student Guesses of Dr. Love's Age in 2024",
       subtitle = "Love's actual age = 57.5 in 2024") +
  theme_bw()

2024 Data, With Better Labels

OK. That’s it for the slides. Back to the Class 02 README.

431 Class 02

Instructions for the Quick Survey

Today’s Agenda

The R Packages I’ll Load Today

Chatfield’s Six Rules for Data Analysis

Our Quick Survey

Types of Data

Continuous vs. Discrete Quantities

Quantitative Variable Subtypes

Qualitative (Categorical) Data

Some Categorical Variables

Are these quantitative or categorical?

Importing and Tidying Data

Ingesting the Quick Surveys

The Quick Survey

Question

The 15 Survey Items

Response to the Question I asked

Guess My Age

English best language?

Height

Handedness Scale (2016-21 version)

Favorite color

Following the Rules? (2019 version)

2019 pulse responses, sorted (n = 61, 1 NA)

Stem and Leaf: Pulse Rates 2014-2023

Garbage in, garbage out …

Group Age Guessing from Photos (13 groups, 10 Photos)

Photos 1-5

Photos 6-10

2024 Groups 1-6: Guessing Ten Photos

2024 Groups 7-13: Ten Photos

Error Distribution, Groups 1-6

Error Distribution, Groups 7/13

Absolute and Squared Errors (first 6)

Absolute and Squared Errors (7-13)

Importing guesses from 2014-2024

2014-2024 Errors

Guessing My Age (Twice) from Class 01

From our 431-Data Page: A .csv file

Creating the age_guess Tibble

The age_guess tibble

How many guesses in each year?

What do the guess1 values look like?

Plot the guess1 values?

Can we make a histogram?

Improving the Histogram, 1

Improving the Histogram, 2

Improving the Histogram, 3

Improving the Histogram, 3

Improving the Histogram, 4

Improving the Histogram, 4

Improving the Histogram, 5

Improving the Histogram, 5

Add title and subtitle (ver. 6)

Add title and subtitle (ver. 6)

Improving the Histogram, 7

Improving the Histogram, 7

In which year did I look older?

In which year did I look older?

Numerical Summary

Let’s Focus on 2024 guesses

First Guesses in 2024

Simple Stem-and-Leaf

Summarizing 2024 Guesses

Summarizing 2024 Guesses

Summarizing 2024 Guesses

How did guesses change in 2024?

How much did guesses change in 2024?

Histogram of Guess Changes

Histogram of Guess Changes

Guess 1 vs. Guess 2 Scatterplot

Filter to complete cases, and add regression line

Filter to complete cases, and add regression line

What is that regression line?

Bayesian linear regression instead?

How about a loess smooth curve?

How about a loess smooth curve?

Add y = x line (no change in guess)?

Add y = x line (no change in guess)?

2019 `pulse` responses, sorted (n = 61, 1 NA)

Group Age Guessing from Photos
(13 groups, 10 Photos)

Guessing My Age (Twice)
from Class 01

From our 431-Data Page: A `.csv` file

Creating the `age_guess` Tibble

The `age_guess` tibble

What do the `guess1` values look like?

Plot the `guess1` values?